Nudging the Aggregative Behavior of Noncooperative Agents

We consider the problem of steering the aggregative behavior of a set of noncooperative price-taking agents to a desired point. Different from prevalent pricing schemes where the price is available for design, we resort to suitable nudge mechanisms to influence the behavior of the agents. In particular, a regulator sends a price prediction signal to the agents, based on which the agents decide on their actions. This prediction is potentially different from the actual price, which brings the issue of reliability. We take this into account by associating trust variables to the agents, implying that the agents do not blindly follow the prediction signal. These trust variables are updated depending on the history of the discrepancy between the actual and the predicted price. We carefully examine the resulting multi-components model and analyse its convergence properties. We show that under the proposed nudge mechanisms, the regulator gains agents' trust fully, and the aggregative behavior provably converges to a desired set point. The effectiveness of the approach is demonstrated by numerical examples.